Nonlinear dynamic behavior of functionally graded beams resting on nonlinear viscoelastic foundation under moving mass in thermal environment

The aim of this paper is to investigate nonlinear dynamic responses of functionally graded composite beam resting on the nonlinear viscoelastic foundation subjected to moving mass with temperature rising. The non-linear strain-displacement relationship is considered in the finite strain theory and the governing nonlinear dynamic equation is obtained by using the Hamilton's principle. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then the governing equation is solved by using of multiple time scale method. The influences of temperature rising, material distribution parameter, nonlinear viscoelastic foundation parameters, magnitude and velocity of the moving mass on the nonlinear dynamic responses are investigated. Also, the buckling temperatures of the functionally graded beams based on the finite strain theory are obtained.